AP EAPCET 19-Aug-2021 Shift 1 Paper

We know that,
r=

m1r1+m2r2+m3r3+...+mnrn

M

...(i)
Let origin be the centre of mass of the body which is represented by C.
i.e. r=0
∴ From Eq. (i), we get
m1r1+m2r2+m1r3+...mnrn=0 ...(ii)
Net moment of all particles in the system about centre of mass C.
τC=m1gr1+m2gr2+m3gr3+...mngrn
=g[m1r1+m2r2+m3r3+...+mnrn]
=g×0 [from Eq. (ii)]
= 0
Hence, sum of moments of all the particles in a system about its centre of mass is always zero.